Problem: Simplify; express your answer in exponential form. Assume $y\neq 0, p\neq 0$. $\dfrac{{(y^{-5})^{4}}}{{(y^{-3}p^{-2})^{-1}}}$
Solution: To start, try working on the numerator and the denominator independently. In the numerator, we have ${y^{-5}}$ to the exponent ${4}$ . Now ${-5 \times 4 = -20}$ , so ${(y^{-5})^{4} = y^{-20}}$ In the denominator, we can use the distributive property of exponents. ${(y^{-3}p^{-2})^{-1} = (y^{-3})^{-1}(p^{-2})^{-1}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(y^{-5})^{4}}}{{(y^{-3}p^{-2})^{-1}}} = \dfrac{{y^{-20}}}{{y^{3}p^{2}}}$ Break up the equation by variable and simplify. $\dfrac{{y^{-20}}}{{y^{3}p^{2}}} = \dfrac{{y^{-20}}}{{y^{3}}} \cdot \dfrac{{1}}{{p^{2}}} = y^{{-20} - {3}} \cdot p^{- {2}} = y^{-23}p^{-2}$.